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Category: Integration

calculus-prove-that-0-1-1-x-p-1-x-q-x-r-1-log-x-dx-log-p-q-r-1-r-p-r-q-r-m-n-1970-

Question Number 116796 by mnjuly1970 last updated on 08/Oct/20 calculusprovethat::$$\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\left(\mathrm{1}−{x}^{{p}} \right)\left(\mathrm{1}−{x}^{{q}} \right){x}^{{r}−\mathrm{1}} }{{log}\left({x}\right)}{dx}\overset{???} {=}{log}\left(\:\frac{\left({p}+{q}+{r}+\mathrm{1}\right){r}}{\left({p}+{r}\right)\left({q}+{r}\right)}\:\right) \